SECONDARY MATH I // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

2.4

READY Topic:''Comparing'arithmetic'and'geometric'sequences.'The$first$and$fifth$terms$of$a$sequence$are$given.$Fill$in$the$missing$numbers$if$it$is$an$arithmetic$sequence.$Then$fill$in$the$numbers$if$it$is$a$geometric$sequence.$$

Example:$'Arithmetic' 4' 84' 164' 244' 324'Geometric' 4' 12' 36' 108' 324'''1.''Arithmetic' 3' ' ' ' 48'Geometric' 3' ' ' ' 48''2.'Arithmetic' B6250' ' ' ' B10'

Geometric' B6250' ' ' ' B10''3.'Arithmetic' B12' ' ' ' B0.75'

Geometric' B12' ' ' ' B0.75''

SET Topic:''Distinguishing'specifics'between'sequences'and'linear'or'exponential'functions.'Answer$the$questions$below$with$respect$to$the$relationship$between$sequences$and$the$larger$families$of$functions.'''4.'If'a'relationship'is'modeled'with'a'continuous'function'which'of'the'domain'choices'is'a'possibility?' A.'' !!|!! ∈ !, ! ≥ 0 ' ' B.' !!|!! ∈ ! '''''''''''''''C.' !!|!! ∈ !, ! ≥ 0 ''''''D.' !!|!! ∈ ! ''5.'Which'one'of'the'options'below'is'the'mathematical'way'to'represent'the'Natural'Numbers?'' A.'' !!|!! ∈ !, ! ≥ 0 ' ' B.' !!|!! ∈ !, ! ≥ 0 '''''''''''''''C.' !!|!! ∈ !, ! ≥ 0 ''''''D.' !!|!! ∈ ! ''

READY, SET, GO! ''''''Name' ''''''Period'''''''''''''''''''''''Date'

x 3 x 3 x 3 x 3

+80 +80 +80 +80

SECONDARY MATH I // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

2.4

6.''Only'one'of'the'choices'below'would'be'used'for'a'continuous'exponential'model,'which'one'is'it?'' A.''! ! = ! ! − 1 ∙ 4, ! 1 = 3' ' B.'! ! = 4!(5)''''''''''''''''' '' C.'ℎ ! = 3! − 5''''''' ' ' ' D.'! ! = ! ! − 1 − 5, ! 1 = 32''7.''Only'one'of'the'choices'below'would'be'used'for'a'continuous'linear'model,'which'one'is'it?'' A.''! ! = ! ! − 1 ∙ 4, ! 1 = 3' ' B.'! ! = 4!(5)''''''''''''''''' '' C.'ℎ ! = 3! − 5''''''' ' ' ' D.'! ! = ! ! − 1 − 5, ! 1 = 32''8.''What'domain'choice'would'be'most'appropriate'for'an'arithmetic'or'geometric'sequence?'' A.'' !!|!! ∈ !, ! ≥ 0 ' ' B.' !!|!! ∈ !, ! ≥ 0 '''''''''''''''C.' !!|!! ∈ !, ! ≥ 0 ''''''D.' !!|!! ∈ ! ''9.''What'attributes'will'arithmetic'or'geometric'sequences'always'have?''' (There'could'be'more'than'one'correct'choice.'Circle'all'that'apply.)''' A.''Continuous' ' B.'Discrete'' C.'Domain:' !!|!! ∈ ! ''' D.'Domain:' !!|!! ∈ ! ''' E.''Negative'xBvalues'' ' F.'Something'constant' ' G.'Recursive'Rule'''10.''What'type'of'sequence'fits'with'linear'mathematical'models?''' What'is'the'difference'between'this'sequence'type'and'the'overarching'umbrella'of'linear'' relationships?'(Use'words'like'discrete,'continuous,'domain'and'so'forth'in'your'response.)''''''''11.''What'type'of'sequence'fits'with'exponential'mathematical'models?''' What'is'the'difference'between'this'sequence'type'and'the'overarching'umbrella'of'exponential'' relationships?'(Use'words'like'discrete,'continuous,'domain'and'so'forth'in'your'response.)'''''''''

SECONDARY MATH I // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

2.4

GO Topic:''Writing'explicit'equations'for'linear'and'exponential'models.'Write$the$explicit$equations$for$the$tables$and$graphs$below.$This$is$something$you$really$need$to$know.$Persevere$and$do$all$you$can$to$figure$them$out.$Remember$the$tools$we$have$used.$(#21$is$bonus$give$it$a$try.)$12.$ x f (x)

2

3

4

5

-4

-11

-18

-25 $

13.$ x f (x)

-1

0

1

2

2/5

2

10

50 $

14.$ x f (x)

2

3

4

5

-24

-48

-96

-192 $

15.$ x f (x)

-4

-3

-2

-1

81

27

9

3 $

$

16'''''''

'

17.'

'

18'

'

19.'

'

20.'

'

21.'

'$

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